SOLUTION: Find the x-intercept(s) of the graph of the function without graphing the function. {{{ f(x) = sqrt(2x+21)- sqrt(2x)-3 }}}

Algebra ->  Radicals -> SOLUTION: Find the x-intercept(s) of the graph of the function without graphing the function. {{{ f(x) = sqrt(2x+21)- sqrt(2x)-3 }}}      Log On


   

Question 629008: Find the x-intercept(s) of the graph of the function without graphing the function.
+f%28x%29+=+sqrt%282x%2B21%29-+sqrt%282x%29-3+
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B21%29-+sqrt%282x%29-3+=+0
sqrt%282x%2B21%29+=++sqrt%282x%29+%2B+3, square both sides
2x+%2B+21+=+2x+%2B+6sqrt%282x%29+%2B+9
6sqrt%282x%29+=+12
sqrt%282x%29+=+2, square both sides
2x+=+4
x+=+2
The x-intercept is 2.
Coordinates: (2,0)
To verify, here's the graph:
+graph%28+300%2C+300%2C+-1%2C+10%2C+-5%2C+4%2C+sqrt%282x%2B21%29-+sqrt%282x%29-3%29+